On ruckle's conjecture on accumulation games

In an accumulation game, the Hider secretly distributes his given total wealth h among n locations, while the Searcher picks r locations and confiscates the material placed there. The Hider wins if what is left at the remaining n - r locations is at least 1; otherwise the Searcher wins. Ruckle's conjecture says that an optimal Hider strategy is to put an equal amount h/k at k randomly chosen locations for some k. We extend the work of Kikuta and Ruckle by proving the conjecture for several cases, e.g., r = 2 or n - 2; n ≤ 7; n = 2r - 1; h ≤ 2 + 1/ (n - r)and n ≤ 2r.The last result uses the Erdo″s-Ko-Rado theorem. We establish a con nection between Ruckle's conjecture and the Hoeffding problem of bounding tail probabilities of sums of random variables.